Sp_4 weight diagrams

Woot! I understand the weight system. My filler material this week will be to make tensor calculations like the ones I did for If ever run dry of ideas, or get tired of other things, I’ll do a few of them.

I’ll make pictures too. They don’t merit their own page so I’ll just tack them onto this post.

Polytope-to-Cycle conversion

As for examples in

1. I’ll consider Weyl polytopes. This should be review for me, so its a good place to start.
2. Then I’ll do a trivial pseudo-Weyl (but non-Weyl) polytope. The pseudo-Weyl polytopes, I don’t know if I’ve worked with their counterparts, so I just say I’ll try a trivial one (not a full hexagon, for example a single point or a line segment or maybe a triangle).
3. Then I don’t see much point in converting any other pseudo-Weyl polytope unless its an MV-polytope — especially since I have them all listed anyway.

Sp_4

Kamnitzer when he’s laying out the basic MV-polytope examples. I don’t really know anything about though I can guess some about its roots from the diagrams he draws. OK, this “question” is vague; basically I’d like to look at in more detail – at least on the level of weights. I suppose I’ll be able to find material on it in Fullton & Harris.

Polytope-to-Cycle conversion

Kamnitzer specifies a formula for converting a polytope, given either by weights or by collections of integers , into subsets of the grassmanian:

Even though the formula makes sense to me I don’t have much of a sense what this means. I’m going to try to do a few examples. Even if I don’t get any answers at least I’ll have some questions which is more than I have now.

Writing up old material

A lot of material, some very scattered and some a little organized, should be written up. Very old material even, before my orals. If ever I can’t find something to do with myself I can always try to write up summaries of what I know about

1. Sheaves,
2. Derived things,
3. Intersection Homology, and
4. newer stuff…